This paper reviews recent advancements in investigating quantum magnets with long-range interactions using Monte Carlo techniques. Long-range interactions are significant in quantum optics and condensed matter physics, offering insights into quantum-critical properties. The authors focus on two main techniques: perturbative continuous unitary transformations and stochastic series expansion quantum Monte Carlo (SSE QMC). The perturbative continuous unitary transformation method applies classical Monte Carlo integration within white graph embedding schemes, enabling high-order series expansions of energies and observables in the thermodynamic limit. SSE QMC, on the other hand, allows calculations on large finite systems, with finite-size scaling used to determine physical properties of the infinite system. These techniques have been successfully applied to one- and two-dimensional quantum magnets with long-range Ising, XY, and Heisenberg interactions on various lattices. The paper also discusses the study of quantum phase transitions above the upper critical dimension and the scaling techniques used to extract quantum critical properties from numerical calculations.This paper reviews recent advancements in investigating quantum magnets with long-range interactions using Monte Carlo techniques. Long-range interactions are significant in quantum optics and condensed matter physics, offering insights into quantum-critical properties. The authors focus on two main techniques: perturbative continuous unitary transformations and stochastic series expansion quantum Monte Carlo (SSE QMC). The perturbative continuous unitary transformation method applies classical Monte Carlo integration within white graph embedding schemes, enabling high-order series expansions of energies and observables in the thermodynamic limit. SSE QMC, on the other hand, allows calculations on large finite systems, with finite-size scaling used to determine physical properties of the infinite system. These techniques have been successfully applied to one- and two-dimensional quantum magnets with long-range Ising, XY, and Heisenberg interactions on various lattices. The paper also discusses the study of quantum phase transitions above the upper critical dimension and the scaling techniques used to extract quantum critical properties from numerical calculations.